math 8 – lesson 2-1 & 2-2 15 homework packet … · web view15-1 what is a system of linear...

Unit 15 Homework Packet

Systems of Two Linear Equations

15-1 What is a System of Linear Equations in Two Variables?15-2 Solving Systems of Linear Equations by Graphing

15-3 Solving Systems of Linear Equations Using Substitution (Day 1)15-3 Solving Systems of Linear Equations Using Substitution (Day 2)15-4 Solving Systems of Linear Equations Using Elimination (Day 1)15-4 Solving Systems of Linear Equations Using Elimination (Day 2)

15-5 Solving Systems Algebraically – Choosing a Method15-6 System of Equations – Word Problems (Day 1)15-6 System of Equations – Word Problems (Day 2)

15-7 Types of Solutions (one, zero, infinite)

Name _____________________________________

Math 7 – Unit 15 (Systems of Two Linear Equations)HW #15-1 - What is a System of Linear Equations in Two Variables?Mrs. Schrader

Name ____________________________________ Period ______ Date ______________

Show your work on all problems.

1) What is a system of equations? ________________________________________________

_____________________________________________________________________________

2) Write your own system of equations example: ______________________________

______________________________

3) Explain why the following is not a system of linear equations.

y = 6x - 18

_____________________________________________________________________________

____________________________________________________________________________

4) Is the following a system of linear equations? Explain your answer.

18 = 3x + 3y2

21 = 2x2 + 5y

_____________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

5) Which of the following represents a system of linear equations?

(A) b = 4a – 7 (C) 6a – 3b b = 3.7a

(B) 11a – 25b = 31 (D) a2 = -9 b = -9 + a

6) Is (9,6) a solution of the system of linear equations?

-3x + y = -21x - y = 3

The solution (9,6) _______________ a solution of the system of linear equations. (is/is not)

7) Is (-5,-6) a solution of the system of linear equations?

x - y = 1-x + 2y = -7

The solution (-5,-6) ___________ a solution of the system of linear equations. (is/is not)

8) Is (10,0) a solution of the system of linear equations?

y = x - 4

y - x = -10

The solution (10,0) ___________ a solution of the system of linear equations. (is/is not)

Math 7 – Unit 15 (Systems of Two Linear Equations)HW #15-2 - Solving Systems of Linear Equations by GraphingMrs. Schrader

Name _______________________________ Period _______ Date ______________

Use pencil and a straightedge for all graphing problems. Remember to show the slope (m) and y-intercept (b). Label both lines and the solution on the graph.

1) Determine the solution of the system of linear equations by graphing. Show both checks.

y = -x + 8


y = 3x + 5y = x + 7

3) Determine the solution of the system of linear equations by graphing. Shows both checks.

y = 3x - 4y = -3x + 2

4) What is the solution of the system represented by the graph?

y = x + 2

y = -x + 4

The solution to the system of equations is __________________________.

Now, show the CHECKS to be sure your solution is correct:

checks: _____________


y – 2 = xy = 4x + 2


y = 4x - 10

y – x = 1


y - x = 3

y = 5

Math 7 – Unit 15 (Systems of Two Linear Equations)HW #15-3 – Solving Systems of Linear Equations by Using Substitution (Day 1)Mrs. Schrader

Name ____________________________________ Period ______ Date ______________

Show all work.

1) Solve the system by using substitution. Check your solution.

y = 2x6x + 7y = 20

The solution to the system of equations is ____________________.

2) Solve the system using substitution. Check your solution.

3x + 5y = 10y = x + 2



y = -24x - 3y = 18



2x – 3y = -1y = x - 1


Math 7 – Unit 15 (Systems of Two Linear Equations)HW #15-3 – Solving Systems of Linear Equations by Using SubstitutionMrs. Schrader

Name ____________________________________ Period ______ Date ______________

Show all work. Remember, you need to solve for x or y first.

1) Solve the system by using substitution. Check your solution.

x – 2y = 152x + 3y = 2



x – y = 112x + y = 19



4x + 3y = -8-8x + y = -12

-


Math 7 – Unit 15 (Systems of Two Linear Equations)HW #15-4 - Solving Systems of Linear Equations Using Elimination (Day 1)Mrs. Schrader

Name _______________________________ Period _______ Date ______________

Show all work.

1) Which system of equations is best solved using elimination?

I. 2x + 4y = 4 II. y = 3x + 4 III. x = 3y + 6 2x - 4y = -4 y = -2x + 4 x = 4y - 6

2) Solve the system of linear equations using elimination. Show both checks.

x + y = 9x - y = 1



2x + 4y = 0-2x + y = 15



-2x + 3y = 402x + 5y = 24


5) Why or why not would the elimination method a good choice for solving the system of linear equations below? Explain your reasoning.

-3x + 4y = 162x – 4y = -10

_____________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

Math 7 – Unit 15 (Systems of Two Linear Equations)HW #15-4 - Solving Systems of Linear Equations Using Elimination (Day 2)Mrs. Schrader

Name _______________________________ Period _______ Date ______________

Show all work. Remember, you will need to multiply one or both of the equations by a constant multiple so that you have opposite like terms.


2x + 5y = 8x + 2y = 8



3x + 4y = 65x + 2y = -4



6x - 2y = 103x - 7y = -19


4) Why would using elimination to solve the following systems of equations be more difficult?

5x – y = 14-5x + 3 = 3y

_____________________________________________________________________________

_____________________________________________________________________________

Math 7 – Unit 15 (Systems of Two Linear Equations)HW #15-5 – Solving Systems Algebraically – Choosing a MethodMrs. Schrader

Name _______________________________ Period _______ Date ______________

Show all work.

1) Which method would be the most efficient method to use to solve the system?

4x + 5y = 227x – 5y = 11

The best method would be the _______________________ method because ______________

_____________________________________________________________________________

_____________________________________________________________________________

2) Which is the best method to solve this system?

2x - 4y = -6-6x - 4y = -38

(A) Substitution (B) Elimination (C) Graphing


x = 4y + 25x + 6y = 46


_____________________________________________________________________________

_____________________________________________________________________________

4) Solve the system of linear equations algebraically using any method you see fit. Show both checks.

2x + 3y = 2x = 2y + 15



y = 2x - 7y = -9x + 1


_____________________________________________________________________________

_____________________________________________________________________________

Math 7 – Unit 15 (Systems of Two Linear Equations)HW #15-6 – System of Equations – Word Problems (Day 1)Mrs. Schrader

Name _______________________________ Period _______ Date ______________

Show all work.

1) A tree that is 2 ft tall is growing at a rate of 1 ft per year. A 6-foot tree is growing at a rate of 0.5 ft per year. Write and solve a system of equations to find the number of years in which the trees will be the same height. How tall will the trees be? Be sure to write let statements. Show both checks.

In __________ years, the trees will both be ______________________ tall.

2) Wildlife biologists studied the weights of two alligators over a period of time. The initial weight of the first alligator was 4 lbs and it grew at a rate of 1.5 lbs per month. The second alligator initially weighed 6 lbs, and grew at a rate of 1 lb per month. Write and solve a system of equations to find the number of months in which both alligators will weigh the same amount. What is the amount that they weighed? Be sure to write let statements. Show both checks.

In __________ months, both alligators will weigh __________________________.

3) Bob and Jennie are reading the same book about dung beetles. Bob is on page 4 and reads two pages every night. Jennie is on page 1 and reads 3 pages every night. After how many nights will Bob and Jennie have read the same number of pages? Write a system of linear equations, and solve graphically. Show both checks.

Math 7 – Unit 15 (Systems of Two Linear Equations)HW #15-6 – System of Equations – Word Problems (Day 2)Mrs. Schrader

Name _______________________________ Period _______ Date ______________

Show all work.

1) Two airplanes are carrying food and medical supplies to a country in need. One airplane is carrying 63 meals and 57 medical kits. The total cost for the supplies on that airplane is $714. The other airplane is carrying 78 meals and 57 medical kits. The total cost for the supplies on that airplane is $789.

Write and algebraically solve a system of linear equations to find the price of one meal and the price of one medical kit. Be sure to write let statements and show both checks.

The cost of one meal is ________________; the cost of one medical kit is ________________.

2) A hotel offers two activity packages. The first activity package costs $192 and includes 3 hours of horseback riding and 2 hours of parasailing. The second activity package costs $213 and includes 2 hours of horseback riding and 3 hours of parasailing. Write and algebraically solve a system of linear equations to find the cost of one hour of horseback riding and one hour of parasailing. Show both checks.

The cost of one hour of horseback riding is _________________

The cost of one hour of parasailing is __________________

3) A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,240 ft. Write and algebraically solve a system of equations to determine the flag’s width and length if the length is 420 feet greater than the width. Show both checks. Be sure to write two let statements.

The flag’s length is ____________________; the flag’s width is ____________________

Math 7 – Unit 15 (Systems of Two Linear Equations)HW #15-7 – Types of Solutions for Systems of Linear EquationsMrs. Schrader

Name _______________________________ Period _______ Date ______________

1) Complete the blanks for each solution.

The equations for one solution have _______________________ slopes. The y-intercepts can

either be the ____________ or ____________________.

The equations for no solution have the _____________ slopes, but ______________________y-intercepts.

The equations for infinitely many solutions have the ___________ slopes and ____________ y-intercepts.

2) Without graphing, decide whether the system of equations has one solution, no solution, or infinitely many solutions.

y = 9x + 7y = -9x + 7

How many solutions does the system of equations have?

(A) Infinitely many solutions

(B) No Solution

(C) One Solution

3) Without graphing the equations, decide whether the system of equations has one solution, no solution, or infinitely many solutions.

4y = x - 7 -8y = -2x + 14



(B) No Solution

(C) One Solution

4) Does this system of have one solution, no solution, or an infinite number of solutions?

x + y = 12x + y = 4



(B) No Solution

(C) One Solution

5) How many solutions does this system have?

x + 5y = 030y = -6x



(B) No Solution

(C) One Solution

6) How many solutions does this system have?

4x + 3y = 136x + 27y = 5



(B) No Solution

(C) One Solution

math 8 – lesson 2-1 & 2-2 15 homework packet … · web view15-1 what is a system of linear...

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